摘要
本文在弹性动力学范畴内,采用复变函数法和Green函数法研究了出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射问题;采用Green函数法和“契合”方法研究了界面附近半圆形脱胶的圆柱形弹性夹杂对SH波的散射问题以及SH波作用下界面附近含有半圆形脱胶的圆柱形弹性夹杂和界面裂纹的相互作用问题。
研究出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射问题。首先,给出在含有半圆形凸起的圆柱形弹性夹杂的弹性半空间中,水平表面上任意一点承受时间谐和的出平面线源荷载作用时的位移函数,取该位移函数作为Green函数。然后,采用分区的思想,分别构造出夹杂内的驻波和夹杂外的散射波,满足公共边界处位移和应力的连续性条件,建立起求解该问题的无穷代数方程组。最后,给出了动应力集中系数和水平地面位移幅值的数值结果,并进行了讨论。
研究SH波对双相介质界面附近含有半圆形脱胶的圆形弹性夹杂的散射问题。首先,沿界面将整个空间分成上下两部分。在下半空间,采用本文中所构造的Green函数,并采用“契合”的方法在上下空间连接时满足界面处连续性条件,构造出半圆形脱胶裂纹,进而求出应力和位移的表达式。最后作为算例,给出了动应力集中系数的数值结果,分析了介质参数和入射波参数对动应力集中的影响情况。
研究SH波对双相介质界面附近含有半圆形脱胶的圆形弹性夹杂的散射问题的远场解。利用Hankel函数在宗量充分大时的渐近表达式,可以得到该问题的散射波远场位移模式和散射截面,分析了不同参数对远场解的影响结果。
研究SH波对双相介质界面附近含有半圆形脱胶及其边缘直线型裂纹的圆柱形弹性夹杂的散射问题。沿界面将整个空间分成上下两部分。采用“契合”的方法和构造裂纹技术将上下空间连接,构造出半圆形脱胶裂纹和直线型裂纹。然后,给出了直线型裂纹的动应力强度因子的数值结果,并进行了讨论。
研究SH波作用下双相介质界面附近含有半圆形脱胶的圆形弹性夹杂和直线型裂纹的相互作用,该问题中的界面裂纹与脱胶边缘脱离。采用Green函数法、复变函数法、“契合”方法以及构造裂纹技术,将问题归结为求解界面裂纹尖端的Ⅲ型动应力强度因子的问题,并对得到的数值结果进行了讨论。
In the elastic dynamics range, the scattering of out-plane line source load by a semi-cylindrical hill of cylindrical elastic inclusion in half space is studied by complex variable method and the Green's Function method; By the Green's Function method and the "conjunction" method, the scattering of SH-wave by an interface cylindrical elastic inclusion with a semicircular disconnected curve, the interaction of an interface cylindrical elastic inclusion with semicircular disconnected curve and linear cracks impacted by SH-wave are investigated.
The scattering of out-plane line source load by a semi-cylindrical hill of cylindrical elastic inclusion in half space is studied by complex variable method and the Green's Function method. Firstly, in the elastic half space with the semi-cylindrical hill of cylindrical inclusion, the arbitrary displacement field while bearing out-plane harmonic line source load at horizontal surface is given as the Green's function. Then, with the method of dividing the district, a standing wave in the inclusion and the scattering wave outside can be constructed seperately. In order to satisfy the continuous condition of the displacement and stress around the common boundary condition, a series of infinite algebraic equations can be obtained to settle this problem. In the end, as examples, numerical results of dynamic stress concentration factor and the ground vibration in the horizontal surface are presented and discussed.
The scattering of SH-wave by an interface cylindrical elastic inclusion with a semicircular disconnected curve near two-phase mediums is researched. Firstly, we can divide the space into up-and-down parts along the interface. In the lower half space, with the suitable Green's function constructed above, the semicircular disconnected curve can be constructed when the two parts are bonded which is continuous in the interface impacted by SH-wave by the "conjunction" method. And the expressions of displacement field and stress field are obtained under this situation. Finally, some examples and results of dynamic stress concentration factor are given and the influences by the difference parameters of mediators and the incident wave are discussed.
The far field solution of SH-wave impacted by a cylindrical elastic inclusion with a semicircular disconnected curve near bi-media material interface. Based on the progressive expression of the Hankel function with the large enough independent variable, The displacement mode of scattered wave at far field and scattering cross-section are given. The influences to the far field solution by different parameters are discussed.
The scattering of SH-wave by an interface cylindrical elastic inclusion with a semicircular disconnected curve and linear cracks originating at the curve near two-phase mediums is investigated. Along the interface, the whole space is divided into two parts. With the "conjunction" method and the method of crack-constitution, the semicircular disconnected curve and the linear cracks are constructed when the two parts are bonded along the interface. Some examples and results of dynamic stress intensify factor are given with discussions.
The interaction of an interface cylindrical elastic inclusion with semicircular disconnected curve and linear cracks impacted by SH-wave is investigated. In this problem, the linear cracks and the disconnected curve is not connected. By the Green's Function method, complex variable method, the "conjunction" method and the method of crack-constitution, the subject is inverted into the solution of the dynamic stress intensityⅢmode of the interface cracks. And some results of dynamic stress intensify factor are discussed.
引文
[1]Pao Y H,Mow C C.Diffraction of Elastic Waves and Dynamic Stress Concentrations.Crane and Russak,New York,1973:114-304P
[2]鲍亦兴,毛昭宙著.刘殿魁,苏先樾译.弹性波的衍射与动应力集中.北京:科学出版社,1993:72-202页
[3]黎在良,刘殿魁著.固体中的波.北京:科学出版社,1995:286-319页,377-431页
[4]钟伟芳,聂国华著.弹性波的散射理论.武汉:华中理工大学出版社,1997:137-189页
[5]王铎,马兴瑞,刘殿魁.弹性动力学最新进展.北京:科学出版社,1995:13-15页
[6]Sezawa K.Scattering of Elastic Waves and Some Allied Problems.Bull.Earthquake.Res.Inst.Tokyo.Imperial.Univ.,1927,3:19P
[7]Wolf A.Motion of a Rigid Sphere in Acoustic Wave Field.Geophysics,1945,10:91P
[8]Nagase M.Diffraction of Elastic Wave by a Sphere Surface.J.Phys.Soc.Japan.,1957,11(3):279P
[9]Knopoff L.Scattering of Compressional Waves by Spherical Obstacle.Geophysics,1959,24(1):30P
[10]Nishimura G,Jimbo Y A.Dynamic Problem of Stress Concentration Stresses in the Vicinity of a Spherical Matter Included in an Elastic Solid Under Dynamical Force.J Faculty of Engineering,Univ of Tokyo,1955,24:101P
[11]Ying C F,Truell R.scattering in an Isotropic Elastic Solid.J.Appl.phys.,1956,27(9):1086-1097P
[12]Einspruch N G,Witterholt E J,Truell R.Scattering of a Plane Transverse Wave by a Spherical Obstacle in an Elastic Medium. J. Appl. Phys., 1960,31(5): 806-818P
[13] Pao Y H, Mow C C. Dynamic Stress Concentration in an Elastic Plate with Rigid Circular Inclusion. Proc 4th National Cong of Appl Mech., 1962: 335P
[14] Mow C C, Mente L J. Dynamic Stresses and Displacements Around Cyindrical Discontinuiti-es due to Plane Harmonic Shear Waves. J. Appl.Mech., 1963,30(4): 598P
[15] White R M. Elastic Wave Scattering at a Cylindrical Discontinuity in a Solid.J. Acoust. Soc. Am., 1958, 30(8): 771P
[16] Kato K. Reflections of Sound Wave due to a Hollow Cylinder in an Elastic body. Mem Inst ci Indus Res. Vol 9 Osaka University Japan, 1952
[17] Baron M L, Mattews A T.Diffraction of a Pressure Wave by a Cylindrical Cavity in an Elastic Medium. ASME. J. Appl. Mech., 1961, 28: 347P
[18] Baron M L, Parnes R, Displacements and Velocities Produced by the Diffraction of a Pressure Wave by a Cylindrical Cavity in an Elastic Medium.ASME. J. Appl. Mech., 1962, 29: 385P
[19] Mow C C. Transient Response of a Rigid Spherical Inclusion in an Elastic Medium. J. Appl. Mech., 1965, 32(3): 637P
[20] Mow C C. On the Transient Motion of a Rigid Spherical Inclusion in an Elastic Medium and its Inverse problem. J. Appl. Mech., 1966,33(4): 807P
[21] Miklowitz J. Scattering of a plane Elastic Compressional Pulse by a Cylindrical Cavity. Proc 11th Int Cong of Appl Mech Munich, 1964: 469P
[22] Norwood F R, Miklowitz J. Diffraction of Transient Elastic Waves by a Spherical Cavity. J. Appl. Mech., 1967, 34(3): 735P
[23] Jain D L, Kanwal R P. Scattering of elastic Waves by Circular Cylindrical Flaws and Inclusions. J. Appl. Phys., 1979, 50(6): 4067-4108P
[24] Jain D L, Kanwal R P. Scattering of Elastic Waves by an Elastic Sphere. Int. J Eng.Sci.,1980,18:829-839P
[25]DATTA S K,SHAH A H.Scattering Of SH-waves By Embedded Cavities.Wave Motion,1982,4:265-283P
[26]Datta S K,Akily N E.Diffraction of Elastic Waves in a Half Space Ⅰ:integral Representations and Matched Asymptotic Expansions in Modern problems in Elastic Wave Propagationed.Miklowitz J.and Achenbach JD.AWiley-Interscience,1978:197-218P
[27]Datta S K,Wong K C,shah A H.Dynamic Stresses and Displacements Around Cylindrical Cavities of Arbitrary Shapes.ASME.J.Appl.Mech.,1984,51:798-803P
[28]黎在良,刘殿魁.各向异性介质中圆柱体对SH波散射的射线理论.地震工程与工程震动,1987,7(1):1-8P
[29]Liu D K,Gai B Z.and Tao G Y,Applications of the Method of Complex Function to Dynamic Stress Concentration.Wave motion,1982,4:293- 304P
[30]刘殿魁,刘宏伟.SH波散射与界面圆孔附近的动应力集中,力学学报,1998,30(5):597-604页
[31]刘宏伟,刘殿魁.界面圆孔对SH波的散射远场解,固体力学学报,1999,20(4):349-355页
[32]刘殿魁,田家勇.SH波对界面圆柱形弹性夹杂散射及动应力集中.爆炸与冲击.1999,19(2):115-123页
[33]Yang Zailin,Liu Dankui.Scattering far field solution of SH-wave by movable rigid cylindrical interface.Acta Mechanica Solida Sinica,2002,15(3):214-220P
[34]刘殿魁,杨在林,刘建百.界面可移动圆柱形刚性夹杂对SH波散射及动应力集中.哈尔滨建筑大学学报.2001,34(6):1-7P
[35]刘殿魁,史守峡.界面上圆形衬砌结构对平面SH波散射,力学学报,2002,34(5):796-803页
[36]史守峡,刘殿魁.SH波与界面多圆孔的散射及动应力集中,力学学报,2001,33(1):60-70页
[37]王志伟,齐辉,刘殿魁.具有刚性覆盖层的界面圆环形衬砌对SH波的散射.哈尔滨工程大学学报.2002,23(4):81-85页
[38]陈志刚,刘殿魁.椭圆孔对SH波散射的远场解.哈尔滨工程大学学报,2003,24(3):334-338页
[39]刘殿魁,林宏.SH波对双相介质界面附近圆形孔洞的散射.固体力学学报.2003,24(2):197-204页
[40]Chen Zhigang,Liu Diankui and Yang Zailin.Dynamic stress concentration and scattering of SH-wave by interface elliptic cylindrical cavity.Earthquake Engineering and Engineering Vibration,2003,Vol2,No.2:299-306P
[41]林宏,史文谱,刘殿魁.SH波入射时浅埋结构的动力分析.哈尔滨工程大学学报.2001,22(6):84-87页
[42]王艳,刘殿魁.SH波入射时浅埋衬砌结构动力分析.哈尔滨工程大学学报.2002,23(6):43-47页
[43]林宏,刘殿魁.半无限空间中圆形孔洞周围SH波的散射.地震工程与工程振动.2002,22(6):9-16页
[44]齐辉,王艳,刘殿魁.半无限空间界面附近SH波对圆形衬砌的散射.地震工程与工程振动.2003,23(3):41-46页
[45]刘殿魁,林宏.浅埋的圆形孔洞对SH波散射与地震动.爆炸与冲击.2003,23(1):6-12页
[46]陈志刚,刘殿魁.SH波冲击下浅埋任意形孔洞的动力分析.地震工程与工程振动.2004,24(4):32-36页
[47]陈志刚,杨在林,刘殿魁.SH波在浅埋椭圆孔上的散射对地震动的影响.哈尔滨工程大学学报.2006,27(2):5-9页
[48]杜永军,赵启成,刘殿魁,王艳,周瑞芬.SH波入射时半圆形凸起地形附近浅埋圆形衬砌的动力分析.地震工程与工程振动.2005,25(3):6-12 页
[49]王慧文,刘殿魁,邱发强,陈海涛.SH波入射多个浅埋圆形衬砌附近半圆形沉积层的地震动.东北林业大学学报.2005,33(6):71-75页
[50]王慧文,刘殿魁,邱发强,任方.SH波入射多个半圆形谷地浅埋圆孔的动力分析.自然灾害学报.2006,15(3):109-115页
[51]王慧文,孙晓娟,刘殿魁.浅埋圆形夹杂附近半圆形沉积层对SH波的散射与地表位移.黑龙江工程学院学报(自然科学版).2006,20(2):1-5页
[52]刘殿魁,吕晓棠.浅埋圆柱形弹性夹杂附近的半圆形凸起对SH波的散射.哈尔滨工程大学学报.2006,27(2):189-194页
[53]刘殿魁,王国庆.浅埋圆形孔洞附近的半圆形凸起对SH波的散射.力学学报.2006,3(2):209-218页
[54]何钟怡,樊洪明,刘有军.SH波绕界面孔的散射.力学学报,Vol34,2002,1:68-75页
[55]梁建文,严林隽,Vincent W.Lee.圆弧形层状沉积谷地对入射平面P波的散射解析解.固体力学学报.2001,23(2):168-184页
[56]梁建文,严林隽.圆弧形凹陷地形表面覆盖层对入射P波的影响.固体力学学报.2002,23(4):397-411页
[57]梁建文,严林隽.圆弧形层状沉积谷地对入射SV波散射解析解.固体力学学报.2003,24(2):235-243页
[58]梁建文,张浩.平面P波入射地下洞室群动应力集中问题解析解.岩土工程学报.2004,26(6):815-819页
[59]梁建文,尤红兵.层状半空间中洞室对入射平面P波的放大作用.地震工程与工程振动.2005,25(2):16-24页
[60]尤红兵,梁建文.层状半空间中洞室对入射平面SV波的散射.岩土力学.2006,27(3):383-388页
[61]梁建文,李艳恒,Vincent W Lee.地下洞室群对地面运动影响问题的级数解答:SH波入射.岩土力学.2006,27(10):1663-1672页
[62]杨彩红,梁建文,张郁山.多层沉积凹陷地形对平面SH波散射问题的解析解.岩土力学.2006,27(12):2191-2196页
[63]Sih,G C.Elastodynamic Crack Problems.Mechanics of Fracture.
[64]Achenbach J D.and Brind R J.Elastodynamic Stress-Intensity Factors for a Crack near a Free Surface.J.Appl.Mech.,1981,48:539-552P
[65]Gautensen A K,Achenbach J D.and Mcmaken H.Surface-Wave Rays in Elastodynamic Diffaction by Cracks.Acoust.Soc.Am.,1978,63:1824-1831P
[66]Achenbach J D,Keer L M.and Mendelsohn DA.Elastodynamic Analysis of an Edge Crack.ASME.J.Appl.Mech.,1980,47:551-556P
[67]Achenbach J D,Adler L,Lewis D K and McMaken H.Diffaction of Ultrasonic Waves by Penny-Shaped Cracks in Metals.Theory and Experiment.J.Acoust.Soc.Am.,1979,64:1848-1856P
[68]Achenbach J D,Li L Z.Propagation of Horizontally Polarized Transverse Waves in a Solid with a Periodic Distribution of Cracks.Wave Motion,1986,8:371-382P
[69]Wickham G R.The Diffraction of Stress Waves by a Plane Finite Crack in Two Dimensions:Uniqueness and Existence.Proc.R.Soc.,1981,A378:241-261P
[70]Gracewski S M and Bogy D B.Elastic Wave Scattering from an Interface Crack in a Layered Half Space Submerged in Water:Part Ⅰ:Applied Tractions at The Liquid-Solid Interface.ASME.J.Appl.Mech.,1986,53:326-332P
[71]Gracewski S M and Bogy D B.Elastic Wave Scattering from an Interface Crack in a Layered Half Space Submerged in Water:Part Ⅱ:Incident Plane Waves and Bounded Beams.ASME.J.Appl.Mech.,1986,53:333-338P
[72]马兴瑞,邹振祝,邵成勋,黄文虎.层状介质交界裂纹的弹性波(P波和SV波)散射研究.航空学报.1989,10:434-447页
[73]Itou,S.Diffraction of an Antiplane Shear Wave by Two Coplanar Griffith Cracks in an Infinite Elasic Medium.Int.J.Solids.Structure.,1980,16:1147-1153P
[74]Srivastava K N,Palaiya R M and Karaulia D S.Interaction of Shear Waves with Two Coplanar Griffith Cracks Situated in an Infinitely Long Elastic-Strip.Int.J.of Fracture.,1983,23:3-14P
[75]Loeber G F and Sih G C.Transmission of anti-plane shear waves past an interface crack in dissimilar media.Eng.Fract.Mech.,1973,Vol5:699-725P
[76]陆建飞,王建华,沈为平.曲线裂纹和反平面圆形夹杂相交问题.固体力学学报.2000,21(3):205-210页
[77]刘殿魁,刘宏伟.孔边裂纹对SH波散射及动应力强度因子,力学学报,1999,31(3):292-299页
[78]史守峡,刘殿魁,杨庆山.SH波对内含裂纹衬砌结构的散射与动应力集中.爆炸与冲击.2000,20(3):228-234页
[79]田家勇,齐辉,刘殿魁.一类复合缺陷对SH波散射及动应力强度因子.哈尔滨工程大学学报.2000,3:52-57页
[80]刘殿魁,陈志刚.椭圆孔边裂纹对SH波的散射及其动应力强度因子.应用数学与力学.2004,25(3):958-966页
[81]李宏亮,刘殿魁.SH波作用下圆形夹杂与裂纹的相互作用.哈尔滨工程大学学报.2004,25(5):618-622页
[82]李宏亮,刘殿魁.SH波作用下裂纹对圆夹杂散射动应力集中问题.哈尔滨工程大学学报.2005,26(3):359-363页
[83]杜永军,赵启成,黄燕,李宏亮,张彦河.裂纹对圆孔SH波散射与动应力集中系数的影响.哈尔滨工业大学学报.2005,37(8):1077-1079页
[84]Yang Zailin,Liu Diankui Lv Xiaotang.Dynamics of a Mode Ⅲ Crack Impacted By Elastic Wave in Half Space with a Removable Rigid Cylindrical Inclusion.Key Engineering Materials,2006.9,V324-325:679-682P
[85]Zailin Yang Zhigang Chen,Diankui Liu.Scattering of SH wave by an interacting mode Ⅲ crack and a circular cavity in half space.Key Engineering Materials,2007.7,V348-349:861-864P
[86]Coussy O.Scattering of SH-waves by a Cylindrical Inclusion Presenting an Interface Crack.OR.Acad.Soc.Paris.,1982,295:1043P
[87]Coussy O.Scattering of Elastic Waves by an Inclusion with an Interface Crack,Wave Motion,1984,6:223P
[88]Yang Y,Norris A.Shcar wave scattering from a debonded fiber.J.Mech.Phys Solids.,1991,39:273P
[89]Norris A,Yang Y.Dynamic stress on a partially bonded fiber.J.Appl.Mech.,1991,58:404P
[90]汪越胜,王铎.剪切波作用下圆弧形界面裂纹的动强度因子.固体力学学报.1993,14(4):362-367页
[91]汪越胜,王铎.SH波对有部分脱胶衬砌的圆形孔洞的散射.力学学报.1994,26(4):462-469页
[92]汪越胜,王铎.P波对界面部分脱胶的刚性圆柱夹杂的散射.应用力学学报.1996,13(1):1-9页
[93]汪越胜,于桂兰,王铎.与土体部分脱离的刚性半圆形基础的出平面响应.工程力学.1997,14(1):26-33页
[94]Trifunac M D.Scattering of Plane SH-waves by a Semi-Cylindrical Canyon.Earthquake Engineering and Structural Dynamics,1973,1:267-281P
[95]Liu Diankui,Han Feng.Scattering of Plane SH-waves by Cylindrical Canyon of Arbitrary Shape in Anisotropic Media.Acta Mechanics Sinica,1990,6(3):256-260P
[96]Liu Diankui,Han Feng.Scattering of Plane SH-waves by a Cylindrical Canyon of Arbitrary Shape.Int.J.Soil.Dynamic and Earthquake Engineering,1991,10(5):249-255P
[97]刘殿魁,许贻燕.各向异性介质中SH波与多个半圆形凹陷地形的相互作用.力学学报.1993,25(1):93-102P
[98]Xiaoming Yuan and Fulu Men.Scattering of Plane SH-waves by a Semi-cylindrical Hill.Earthq.Eng.and Struct.Dynamics.,1992,21:1091-1098P
[99]崔志刚,曹新荣,刘殿魁.SH波对半圆形凸起地形的散射.地震工程与工程振动.1998,18(1):140-146P
[100]刘殿魁,曹新荣,崔志刚.多个半圆形凸起地形对平面SH波散射.固体力学学报.特刊,1998:178-185P
[101]郭敦仁编.数学物理方法.第一版.人民教育出版社,1998:333页
[102]张石生.积分方程.重庆,重庆出版社,1958
[103]Sih G C,ed.Mechanics of Fracture.vol.1[M].Leyden:Noordhoff.1973
[104]Loeber J F and Sih G C.Diffraction of Antiplane Shear Waves by a Finite Crack.Journal of the Acoustical Society of America,1968,44(1):90-98P
[105]史守峡,杨庆山,刘殿魁,齐辉.SH波对圆形夹杂与裂纹的散射及其动应力集中.复合材料学报.2000,17(3):107-112页
[106]Sih G C,ed.Mechanics of Fracture.Vol.4.Leyden:Noordhoff.1977
[107]Sih G C,ed.Mechanics of Fracture.Vol.6.Cracks in Composite Material.Leyden:Noordhoff.1981
[108]Sih G C.Stress distribution near internal crack tips for longitudianl shear problems.ASME.Journal of Applied Mechanics,1965,32(1):51-58P
[109]李宏亮.SH波作用下孔洞、夹杂与直线形裂纹的相互作用.哈尔滨工程大学博士学位论文.2004,11:33-36页
[110]Gubernatis J E,Domany E,Krumhansl J A and Huberman M.The Born Approximation in the Theory of the Scattering of Elastic Waves by Flaws.Journal Applied Physics,1977,48:2812-2819P
[111]Mal A Kand Knopoff L.Elastic Wave Velocities in Tow-Component Systems.J.of Inxtitute of Appl.Math.,1976,3:376-387P
[112]Waterman P.Matrix Theory of Elastic Wave Scattering.Journal Acoustical Society of America,1976,60:567-580P
[113]Pao Y H.Betti's Identity and Transition Matrix for Elastic Waves,I.Theory.Journal Acoustical Society of America,1976,60:556-556P
[114]Achenbach J D,Gautesen A K and McMaken H.Ray Method for Waves in Elastic Solids with Application to Scattering by Cracks.Pitman Advanced Publishing Progran,Boston.1982
[115]刘殿魁,盖秉政,陶贵源.论孔附近的动应力集中.力学学报特刊1981,65-77页
[116]Liu D K,Gai B Z and Tao G Y.Applications of the Method of Complex Functions to Dynamic Stress Concentrations.Wave Motion,1982,4:293-304P
[117]胡超,刘殿魁.无限大板开孔弹性波的散射及动应力集中.力学学报.特刊.1995
[118]Liu D K and Hu C.Scattering of Flexural Wave and Dynamic Stress Concentration in Mindlin's Thick Plates With a Cutout.Acta Mechanica Sinica,1996,12(2):169-185P
[119]Liu D K.and Song T S.Stress Concentrations of Cylinder with Large Opening.Acta Mechanica Sinica,1997,10(3):214-230P
[120]廖振鹏著.工程波动理论导论.第二版.北京:科学出版社.2002:141-187页
[121]Noble B.Methods on the Wiener-Hopf Technique.Pergamon Press.New York.1958
[122]Sih G C,ed.Mechanics of Fracture.Vol.6.Cracks in Composite Material.Leyden:Noordhoff.1981
[123]Shi G C and Loeber J F.Wave Propagation in Elastic Solid with a Line of Discontinuity or Finite Crack.Journal of Applied Mechanics,1969,27:193-213P
[124]林宏.界面裂纹及其附近的圆形孔洞对SH波的散射.哈尔滨工程大学博士学位论文.2001.
[125]王铎.断裂力学(上).哈尔滨工业大学出版社.1989:117-124页
[126]王竹溪,郭敦仁.特殊函数概论.北京大学出版社,2000:337-417页,601-620页
[127]阿肯巴赫.J.D著.徐植信译.弹性固体中波的传播.上海.:同济大学出版社,1992:279-284页
[128]徐植信.弹性波传播理论一些问题的研究现状和展望.上海力学.1989,10(3):6-10页
[129]王仁等.第十九届国际理论与应用力学大会(ICTAM)情况介绍.力学与实践,1997,19(1):57-64页
[130]郑哲敏,周恒,张涵信,黄克智,白以龙.21世纪初的力学发展趋势.力学进展,1995,25(4):433-449页
[131]#12
[132]Loeber J F and Shi G C.Diffraction of Anti-plane Shear Waves by a Finite Crack.Journal of the Acoustical Society of America,1968,44(1):90-98P
[133]张石生.积分方程.重庆,重庆出版社,1985:77-124页
[134]黄克智,徐秉业.固体力学发展趋势.北京:北京理工大学出版社,1995:33-45页
[135]林成森编著.数值计算方法(下册).科学出版社,1999:60-95页
[136]范天佑编著.应用断裂动力学基础.北京理工大学出版社,1992:99-100页,112-114页
[137]史文谱.含孔半空间中稳态P波的散射.哈尔滨工程大学博士学位论文.2001.
